1. Field of the Invention
The present invention relates to the system employed and circuitry used with an ensemble of clocks to obtain an ensemble time. More particularly, the present invention relates to an improved algorithm defining ensemble time that can be, for example, implemented with Kalman filters for obtaining an improved estimate of time from an ensemble of clocks.
2. Description of the Related Art
For a number of years, groups of precision clocks used in combination have provided the "time" in situations in which high precision timekeeping is required. For example, an "official" time for the United States is provided by the atomic time scale at the National Bureau of Standards, the UTC(NBS), which depends upon an ensemble of continuously operating cesium clocks. The time interval known as the "second" has been defined in terms of the cesium atom by the General Conference of Weights and Measures to be the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. Other clocks may be calibrated according to this definition. Thus, while each clock in a group or ensemble of clocks is typically some type of atomic clock, each clock need not be a cesium clock.
Even though one such atomic clock alone is theoretically quite accurate, in many applications demanding high accuracy it is preferred that an ensemble of atomic clocks be used to keep time for a number of reasons. Typically, no two identical clocks will keep precisely the identical time. This is due to a number of factors, including differing frequencies, noise, frequency aging, etc. Further, such clocks are not 100% reliable; that is, they are subject to failure. Accordingly, by using an ensemble of clocks in combination, a more precise estimate of the time can be maintained.
When an ensemble of clocks is utilized to provide an estimate of time, various techniques may be employed for processing the signals output by the clocks to obtain the "time". Typically, interclock time comparisons are made to determine the relative time and frequency of each clock. The noise spectrum of each clock is represented by a mathematical model, with noise parameters determined by the behavior of the individual clock. Clock readings are combined based on these comparisons and models to produce the time scale.
One technique for processing clock readings involves the use of Kalman filters. Kalman filters have a number of favorable characteristics that lend them to use in timekeeping. Most important of these characteristics are that Kalman filters are minimum squared error estimators and are applicable to dynamic systems. Starting with a physical model for each clock and the definition of an ensemble of clocks, Kalman filters may be used to perform the calculation of the estimated time.
Among their capabilities, Kalman filters produce estimates which are optimum in the minimum squared error sense both in steady state and transient condition. Thus, Kalman filters provide the state estimation and forecasting functions necessary for processing data from an ensemble of clocks. The use of actual system dynamics in the estimation process stabilizes the state estimates against occasional large measurement errors, as Kalman filters automatically provide estimates of the errors of each component of the state vector.
Of course, the goal in any technique used to process clock outputs is to obtain the most uniform scale of time. Generally, the performance of any such technique depends on the realism of the mathematical models used to describe the clocks of the ensemble and the definition of the time scale. In this regard, previously utilized algorithms have failed to provide a complete definition of ensemble time. That is, such definitions have accounted for time state only.
Of importance, prior designers have not fully accounted for the frequency states of member clocks with respect to the ensemble. More particularly, previous algorithms have effectively failed to fully define and employ correlations between the relative states of the clocks with respect to the ensemble. Thus, when a Kalman or any other approach using these definitions has been used, the accuracy of the resulting estimates of clock frequency and estimates of clock parameters has suffered, adversely impacting timekeeping performance.
In theory, such deficiencies decrease as the degree of clock identity in an ensemble increases and as the number of clocks in an ensemble increases. However, in practice, the clocks of an ensemble will not be identical, and a finite number of clocks must be used. Typically, each clock in an ensemble performs differently from the others, even if they are all the same type of clock. Therefore, practically speaking, an inadequacy exists in the prior approaches.
The deficiencies of prior approaches can be described with reference to signal processing in general. As with any type of signal processing, when a filter does not provide the appropriate filter characteristics, the accuracy of the results from processing will be sub-optimal. In the prior approaches, the ensemble definition was incomplete. Accordingly, the accuracy of the estimates of time resulting from use of the corresponding filters suffered.